Worked solution
Discard an always-positive factor safely
Self-Practice 1: solve .
CJC · Lecture · Self-Practice 1
Use a factor whose sign is known
Since x²+1>0 for every real x, division by it preserves the inequality. Thus 4 x²−1≥0, or (2 x−1)(2 x+1)≥0. This holds outside the two roots, including both endpoints: x≤−1/2 or x≥1/2.
How did this part go?
Common mistakes
Cancelling x²+1 is safe because it is strictly positive, unlike the unknown-sign factor in Example 3.